Digit Frequency in 2 Parts

Digit Frequency
What digit is the most frequent between the numbers 1 and 1,000 (inclusive)?

What digit is the least frequent between the numbers 1 and 1,000?

To solve this riddle you don’t want to manually do all of the math but rather try to figure out a pattern.

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  1. I would guess ‘1’ is most frequent and ‘0’ is least frequent.

    I’m guessing there is only one more ‘1’ than there are most other digits (because 1000 is the only 4-digit number, and it has a 1 in it), but there may be a few less 0’s (because no number starts with a 0).

  2. Brent, you are today’s winner and it is good to see you are having fun with the Math riddles.
    The most common digit is ‘1.’ 0 is the least common digit even though 1,000 has three zero’s ! The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers. For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32. However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place. So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first ‘1’ in a new series of ten! In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences. The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc..

  3. The most used number between 1 and 1,000 is 1, on the contrary, the least used number is 0.

  4. I would guess that 1 is the most frequent digit and 0 is the least frequent digit.
    I’m guessing there is only one more ‘1’ than there are most other digits (because 1000 is the only 4-digit number, and it has a 1 in it), but there may be a few less 0’s (because no number starts with a 0).
    The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers. For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32. However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place. So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first ‘1’ in a new series of ten! In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences. The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc..

  5. The question is what number is most frequent BETWEEN 1 and 1000, so 1 and 1000 are not included. That would mean no numbers are more frequent, only 0 is the most infrequent.

  6. Depends if you are counting digital or analogue. If digital then 1 (in a count up to 1000) would appear as 0001, 10 as 0010 etc. Hence on a digital count, 0 is the most frequent digit to appear. As with everything it is a matter of perspective.

  7. 0,10,20,30,40
    1,10,11,12,13,14,16,17,18,19,21,31,41
    2,12,20,21,22,42
    3,13,23,30,31,32,33,43
    4,14,24,34,44
    5,15,25,35
    6,16,26,36
    7,17,27,37
    8,18,28,38
    9,19,29,39

  8. Completely WRONG!
    The question was what number is the most frequent BETWEEN 1-1000.
    Not including. 1 and 1000
    Between 0-1001 is I guess what U meant to ask !

    One is incorrect.

  9. Between 0 and 9 written [0,9] each digit appears once.
    In [10,19] each digit appears once in the singles digit and 1 appears ten additional times in the tens digit
    This pattern will repeat for each digit 2 through nine in the decades [20,29], [30,39] … [90,99]..
    So, at the end, reaching 99 each digit 1 through 9 will have appeared once in each decade, and an additional 10 times in one decade. 0 will obviously be the loser here – it does not appear an additional ten times as it is generally just not written in the first decade (the number 2 is not written 02)
    Nothing will change when we look at centuries. 0 will fall further behind.
    at 999 all digits 1 through nine are equally represented.

    Now eliminate 0 and add 1000 and clearly 1 is the winner. 0 the loser and all others tied

  10. be·tween
    /b??tw?n/
    preposition
    preposition: between; preposition: bet.

    1.
    at, into, or across the space separating (two objects or regions).
    “the border between Mexico and the United States”
    synonyms: in the space separating, in the middle of, with one on either side; More
    amid, amidst;
    archaicbetwixt
    “Philip stood between his parents”
    2.
    in the period separating (two points in time).
    “they snack between meals”
    3.
    in the interval separating (two points on a scale).
    “a man aged between 18 and 30”

    adverb
    adverb: between; adverb: bet.

    1.
    in or along the space separating two objects or regions.
    “layers of paper with tar in between”
    2.
    in the period separating two points in time.
    “sets of exercises with no rest in between”

    if it is between how can it include the boundaries?

  11. Answer using Ruby programming language:

    rubyhome > (1..1000).map { |i| i.to_s.split('') }.flatten.each_with_object(Hash.new(0)) { |i, hsh| hsh[i] += 1 }

    => {"1"=>301, "2"=>300, "3"=>300, "4"=>300, "5"=>300, "6"=>300, "7"=>300, "8"=>300, "9"=>300, "0"=>192}